Only 3 to 4 percent of government operations are on the cloud, creating costs that are "orders of magnitude" higher than the private sector, according to Chris Liddell, director of strategic initiatives for President Donald Trump's administration.

"Virtually none" of the government is on the cloud, Liddell told CNBC's "Squawk on the Street" on Monday. "It's tiny, very small compared to the private sector, and that's one of the real opportunities."

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White House Director of Strategic Initiatives Chris Liddell (L) talks with White House Director of the National Economic Council Gary Cohn before a meeting with small business people in the Roosevelt Room at the White House January 30, 2017 in Washington, DC.

"We are really going to try to push as hard as we can. You'd be blown away by some of the statistics," Liddell said. "We have something like 6,000 data centers across the government. We spend $86 billion a year, and that probably understates the figure, on IT. ... Those are orders of magnitude higher than anything you would see in the private sector. So there's a massive economic opportunity here."

He also noted that moving more government services to the cloud could help with cybersecurity.

Technology executives from Apple, Amazon, Oracle and other American companies are expected to gather at the White House on Monday in a summit aimed at modernizing the government. Liddell, who helped steer Microsoft through a difficult transition during the financial crisis as the company's chief financial officer, said about 90 percent of those invited will be in attendance, a higher turnout than average.

Ultimately, the government, not the private sector, will be responsible for delivering on the recommendations that come out of Monday's summit, Liddell said. But many of the companies, such as Amazon, are considered top cloud services providers.

"We have 3.5 trillion dollars of market value arriving today," Liddell said. "Having those people and the power of their ideas — and the power of, hopefully, some of their people over the next few months and years — we think we can really accelerate what we're doing."

Liddell said part of the goal at the White House is to inspire a dedicated "government tech" industry in the private sector.

"We're 10 to 20 years behind, so we're not going to solve this today," he said.